Question: $\begin{aligned} &f(a)=3a-8 \\\\ &g(b)=\sqrt{14-b}-10 \end{aligned}$ $(g\circ f) (-9)=$
Solution: Let's start by rewriting $(g\circ f) (-9)$ as $g(f(-9))$. When evaluating composite functions, we work our way inside out. To evaluate $g(f(-9))$, let's first evaluate $f(-9)$. Then we'll plug that result into $g$ to find our answer. Let's evaluate $f({-9})$. $\begin{aligned}f(a)&=3a-8\\\\ f({-9})&=3({-9})-8~~~~~~~~~~\text{Plug in }a={-9}\\\\ &=-27-8\\\\ &={-35}\end{aligned}$ We now know that $g(f({-9}))$ is the same as $g({-35})$ because $f({-9}) = {-35}$. Let's evaluate $g({-35})$. $\begin{aligned}g(b)&=\sqrt{14-b}-10\\\\ g({{-35}})&=\sqrt{14-({-35})}-10~~~~~~~~~~\text{Plug in }b={-35}\\\\ &=\sqrt{49}-10\\\\ &=7-10\\\\ &=-3\\\\\end{aligned}$ The answer: $(g\circ f)(-9) =-3$